GaN-based heterostructure devices are of interest for pressure and stress sensing applications due to their potential for use at high temperatures and in caustic environments. We have grown n-GaN/u-AlGaN/n-GaN heterostructure devices on sapphire substrates by organometallic vapor phase epitaxy (OMVPE) using the epitaxial layer overgrowth (ELO) method. The devices were fabricated with varying AlGaN layer thickness and composition. Current-voltage (I-V) characteristics were obtained to characterize the performance of these devices under hydrostatic pressures up to 500 MPa. For a fixed bias, the current was observed to decrease in magnitude with increasing hydrostatic pressure for all devices tested. The current modulation is attributed to piezoelectric effects. Specifically, the polarization charge densities at both GaN/AlGaN interfaces are sensitive to changes in the hydrostatic pressure, and these charges affect the shape of the potential barrier and the current. Changes in the AlGaN layer thickness and composition modify the interfacial polarization, with thicker AlGaN layers and higher Al content increasing the effect of pressure on the observed I-V characteristics. The decreases in current magnitude with increasing pressure are linear over the pressure range tested. In order to quantify the performance of these devices, we calculate a pressure gauge factor based on a normalized change in current divided by the change in pressure. Values obtained range from 0.1-1.0 GPa-1, consistent with our previously published results for a single device. In addition, the turn-on voltages under both forward and reverse bias conditions are observed to increase with increasing AlGaN layer thickness and composition, a result that agrees with our device model. These turnon voltages are governed by different mechanisms in the forward and reverse bias directions. Under forward bias, the mechanism is a transition from a thermionic to a tunneling process. However, under reverse bias, the turn-on occurs when the total electric field changes sign in the AlGaN layer.